I know there is a word beginning with the letter B for someone who loves war and loves to conjure up support of war?
I think you're looking for bellicose.
So: "a bellicose person".
As well, you could use the noun form , "bellicosity", to refer to a person's disposition.
NB: There is no agent form of bellicose, nor usage of the adjective as noun (see: He's a belligerent, don't listen to him.)
"Belligerent" is not a bad choice. I've heard it used to describe people who like to fight and/or engage in war. However, that usage is kind of a stretch. It really only means "engaged in war" (whether you like it or not).
A better choice would be "warmonger," which refers to a person who "encourages warfare" (which is closer to the "lover of war" that you asked about).
I hope this helps :)